A mechanism leading to q-power law distribution due to the inhomogeneity of phase space in the self-gravitational system

One mechanism leading to the q-power law distribution has been proposed in the self-gravitational system. The friction force in the stochastic process may be nonlinearly relevant to the momentum of particle, whose friction coefficient can be expressed as the function of the kinetic energy of the particle. The correlation strength of noises is inhomogeneous in the such system, maybe due to the strength of gravitational field. This implies that the gradient of correlation strength is the function of gravitational force. With the Taylorʼs low order approximation, the stationary solution of the two-vector variable Fokker-Planck equation is the power law form in self-gravitational system. This Letter also verifies that the neutrino flux deviation from the theory value in the solar core is due to the same mechanism.